Heralded entanglement transfer from entangled atomic pair to free electrons

Entangled free electrons constitute a key missing resource for quantum electron optics, with direct relevance to nonclassical electron probes, collective radiation, and quantum-enhanced electron-matter spectroscopy. We propose a heralded protocol for generating Bell pairs of spatially separated free electrons by transferring entanglement from an atomic two-level-system (TLS) pair to electronic energy-sideband degrees of freedom. Local resonant electron-TLS exchange converts a delocalized atomic excitation into a delocalized electronic sideband excitation, and a projective TLS measurement certifies successful Bell-pair generation. A self-contained input-output theory establishes the conditional transfer map, the heralding probability, and the relation between the initial atomic resource and the heralded electronic entanglement. Full-Hamiltonian simulations confirm the robustness of the protocol against detuning, pulse shaping, and counterrotating corrections, with the dominant beyond-rotating-wave approximation effects identified as a Bloch-Siegert-type shift and weak leakage outside the target manifold. The results establish a quantitative route to certifiable entangled free electrons and provide a foundation for integrating stationary quantum resources into nonclassical quantum electron optics.